All the things they beg to be free takes someone's time to produce.
It's only fair that if these people have to give their time for free, people wanting free stuff should start by refusing pay for their time.
But they won't because we all know it's all about "give me free" anyway.
I don't see how this is an issue restricted to socialised healthcare. A workforce shortage can happen regardless of how you handle healthcare.
I'd also add that if it is a violation of rights that patients are not offered equal treatment due to staff shortages, surely it is far worse to have a system designed around only catering to people who can afford healthcare. We have had issues in the UK with a lack of medical staff over the past few years, something that has oddly improved during covid because it raised interest in working for the NHS. It isn't because the system is bad, it is because it has been constantly underfunded for the past 10 years in an attempt by our conservative government to start privatising various branches of it.